@incollection {1217131, title = {The symbolic model for algebra: functions and mechanisms}, booktitle = {Model-Based Reasoning in Science and Technology}, volume = {314}, year = {2010}, pages = {519{\textendash}532}, publisher = {Springer}, abstract = {

The symbolic mode of reasoning in algebra, as it emerged during the sixteenth century, can be considered as a form of model-based reasoning. In this paper we will discuss the functions and mechanisms of this model and show how the model relates to its arithmetical basis. We will argue that the symbolic model was made possible by the epistemic justification of the basic operations of algebra as practiced within the abbaco tradition. We will also show that this form of model-based reasoning facilitated the expansion of the number concept from Renaissance interpretations of number to the full notion of algebraic numbers.

}, isbn = {9783642152221}, url = {http://dx.doi.org/10.1007/978-3-642-15223-8\_29}, author = {Heeffer, Albrecht}, editor = {Magnani, Lorenzo and Carnielli, Walter A. and Pizzi, Claudio} } @incollection {924546, title = {Strategies: what{\textquoteright}s in a name?}, booktitle = {The Many Sides of Logic}, series = {Studies in Logic}, volume = {21}, year = {2009}, pages = {287{\textendash}306}, publisher = {College Publications}, abstract = {

In this paper, I will show that Hintikka’s notion of ‘strategy’ can refer to proof-heuristic reasoning as well as to methodological reasoning forms. Stating this distinction allows for a better understanding of the notion and for an easier way to tackle the problem of formalization. Contrary to Hintikka’s opinion, heuristic reasoning can be implemented in formal proofs by means of goal-directed proof procedures. Methodological reasoning forms on the other hand can be formally represented by means of adaptive logics.

}, isbn = {9781904987789}, author = {Provijn, Dagmar}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @incollection {D:camp, title = {On some Remarkable Relations between Paraconsistent Logics, Modal Logics, and Ambiguity Logics}, booktitle = {Paraconsistency. {T}he Logical Way to the Inconsistent}, year = {2002}, pages = {275{\textendash}293}, publisher = {Marcel Dekker}, address = {New York}, abstract = {

This paper concerns some connections between paraconsistent logics, modal logics (mainly S5), and Ambiguity Logic AL (Classical Logic applied to a language in which all letters are indexed and in which quantifiers over such indices are present). S5 may be defined from AL.

Three kinds of connections are illustrated. First, a paraconsistent logic A is presented that has the same expressive power as S5. Next, I consider the definition of paraconsistent logics from S5 and AL. Such definition is shown to work for some logics, for example Priest{\textquoteright}s LP. Other paraconsistent logics appear to withstand such definition, typically those that contain a detachable material implication. Finally, I show that some paraconsistent logics and inconsistency-adaptive logics serve exactly the same purpose as some modal logics and ampliative adaptive logics based on S5. However, they serve this purpose along very different roads and the logics cannot be defined from one another.

The paper intends to open lines of research rather than pursuing them to the end. It also contains a poor person{\textquoteright}s semantics for S5 as well as a description of the simple but useful and powerful AL.

}, author = {Batens, Diderik}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} }